How would you design routing to meet the above requirements?

Explanations:

This option configures a single routing table with a default route via the Internet gateway but does not propagate specific routes for the on-premises network, which could lead to a lack of routing for traffic from the on-premises network to the application instances in the VPC.

This option allows for a single routing table with a default route to the Internet via the Internet gateway and propagates specific routes for the on-premises networks via BGP. This ensures that both Internet and on-premises traffic can access the application instances appropriately.

This option suggests a single routing table with two default routes, which is not valid. A routing table cannot have multiple default routes; instead, it should have specific routes for the on-premises network and the Internet, and priority must be defined.

This option proposes two routing tables, one for the Internet and one for the on-premises network. However, this could complicate routing and may lead to issues in traffic management since multiple routing tables cannot be effectively managed in this scenario without route prioritization.